What does this research mean for the field?

Coherent-state path integrals yield results identical to those obtained from the canonical Hamiltonian approach in quantum thermodynamics. Novelty: ClaimNovelty.CONFIRMATORY. Consensus alignment: ConsensusAlignment.SUPPORTS_CONSENSUS.

What question did this study set out to answer?

This work aims to clarify the nuances of coherent-state path integrals in quantum thermodynamics.

February 20, 2026Open Access

Coherent-state path integrals in quantum thermodynamics

Key Points

This work aims to clarify the nuances of coherent-state path integrals in quantum thermodynamics.
Focused on evaluating path integrals in continuum across imaginary time and Matsubara-frequency space.
Presented examples using bosonic and fermionic harmonic oscillators, Bose-Hubbard and Hubbard models.
Included weakly-interacting Bose gas and BCS superconductor with finite-range interactions.
Demonstrated that proper handling of path integrals results in outcomes equivalent to canonical Hamiltonian methods.
Illustrated through various respected quantum systems, ensuring the validity of the approach.

Abstract

In these notes, we elucidate some subtle aspects of coherent-state path integrals, focusing on their application to the equilibrium thermodynamics of quantum many-particle systems. These subtleties emerge when evaluating path integrals in the continuum, either in imaginary time or in Matsubara-frequency space. Our central message is that, when handled with due care, the path integral yields results identical to those obtained from the canonical Hamiltonian approach. We illustrate this through a pedagogical treatment of several paradigmatic systems: the bosonic and fermionic harmonic oscillators, the single-site Bose-Hubbard and Hubbard models, the weakly-interacting Bose gas with finite-range interactions, and the BCS superconductor with finite-range interactions.

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